My son (just turned two), used a pacifier all the time. At home during the day, at night, and in the car. Slowly we restricted the use to nap/bed and car use only. Than we slowly took it away for nap time, than car and than bed. It was rough, he would lay in his crib and yell I want my pacifier...but we stuck with it and never gave in. In the car was the hardest because it was distracting listening to him yell and scream for it.
I would let your daughter continue using it, put more than one in her crib so she can find one if she needs/wants it. If she does wake up during the night and you dont want to give her the pacifier, try rubbing her back and telling her its sleepy time. Introduce a stuffed animal or toy she can take to bed with her, that should help her soothe herself too.
If your set on weaning her from it, dont cut the tip, shes too young for that and its a choking hazard. Go cold turkey but be prepared for long nights of crying and not sleeping (or she could pleasantly surprise you).